Algebra 2 help

Question

0

501

2

+18

Problem: If $log{}_{2}x=7$ ,find $log{}_{8}x.$

I am not allowed to use a calculator on this problem.

These are steps I have so far:

2⁷=x

x=128

log₈128=y

8^y=128

y= $\frac{log 128}{log 8}$

And this is where I am stuck. I have to use a calculator for this part. Is there a way to solve this without using a calculator?

Thanks.

LightningSidd Jun 19, 2021

amygdaleon305 · Answer 1 · 2021-06-19T05:09:19

So far, you're doing really well..

After $y = {log128\over log8}$ you don't really need a calculator to solve this

We can write this as

$y= {log 2^7\over log 2^3}$ right?

then $y= {7log2\over 3log2}$

⇒ $y={7\over 3}$

${log}_{8}x = {7\over 3}$

Hope you got it :)